A new numerical relativity-inspired method achieves exponential convergence for scalar self-force calculations in Kerr spacetime on circular equatorial orbits up to near-extremal spins and the ISCO.
Second-order perturbation theory: the problem of infinite mode coupling
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
citation-role summary
background 1
citation-polarity summary
fields
gr-qc 3verdicts
UNVERDICTED 3roles
background 1polarities
background 1representative citing papers
Multiple Hamiltonian definitions of the conservative second-order self-force are identified in a nonlinear scalar toy model, restricted to unbound scattering trajectories.
Extended 1PA self-force waveforms for slowly spinning primary and precessing secondary, with re-summed 1PAT1R variant showing improved accuracy against NR for q ≳ 5 and |χ1| ≲ 0.1.
citing papers explorer
-
Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
Extended 1PA self-force waveforms for slowly spinning primary and precessing secondary, with re-summed 1PAT1R variant showing improved accuracy against NR for q ≳ 5 and |χ1| ≲ 0.1.